CONTINUOUS TIME MIXED STATE BRANCHING PROCESSES AND STOCHASTIC EQUATIONS

doi:10.1007/s10473-021-0504-7

Abstract

Abstract: A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup. Meanwhile, we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.

Key words: mixed state branching process, weak convergence, stochastic equation system, Wasserstein-type distance, stationary distribution

CLC Number:

60J80

Shukai CHEN, Zenghu LI. CONTINUOUS TIME MIXED STATE BRANCHING PROCESSES AND STOCHASTIC EQUATIONS[J].Acta mathematica scientia,Series B, 2021, 41(5): 1445-1473.

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